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Obj1thru8F11

# Obj1thru8F11 - MAC 1105 Lecture Outlines for Ms...

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Unformatted text preview: MAC 1105 Lecture Outlines for Ms. Blackwelder’s lecture classes These notes are prepared using software that is designed for typing mathematics, but produces a pdf output. Alternative format is not available. (Text based file supplied to visually impaired students upon request.) First, we will look at 2 skills that will be used in upcoming objectives. These preliminary objectives may appear on quizzes, but will not be specific test questions. They will be tested as they are used in other objectives. —————————————————————————————————————– Preliminary Objective 1 The relationship between a − b and b − a − 1( a − b ) = − 1( b − a ) = Conclusion? They are or of each other. Simplify. 5 − 5 = − 8 8 = x − 1 1 − x = 3 − 2 x 2 x − 3 = Note. a + b b + a = —————————————————————————————————————– Preliminary Objective 2 Factoring Quadratic Trinomials Note: Many of the problems in our course contain a “hint” for the trinomial factoring. Use It! Before we factor, recall how to multiply two binomials. F O I L Multiply. (6 x − 5)(2 x + 3) (6 x − 5)(2 x − 3) We’ll use Reverse F O I L in order to factor. For some problems, one factor will be known - you will need to determine the other. For some problems, you will factor with no “hint”. An eGrade example. For 18 x 2 − 19 x − 12, one of the factors is 2 x − 3, find the other factor. 18 x 2 − 19 x − 12 = This eGrade problem is in Ntuple mode - enter an ordered pair. Factor. 18 x 2 − 51 x + 8 24 x 2 − 7 x − 5 These eGrade problem are in MultiFormula mode; enter factors separated by semicolon. 1 Objective 1 Rational Expressions - fractions made up of . Obj 1a Recognizing Equivalent Rational Expressions In particular, dealing with a pesky minus sign when it appears in front of a fraction. Consider a numerical fraction − 2 3 We will ask “Which are equivalent to” the given expression, and the problems will be in eGrade Multiple Selection mode. You will choose all that are equivalent; if none are, then select that choice. *************** Plan of Attack Generate equivalent expressions by distributing the minus through the , then separately through the . Compare these with the answer choices. Keep in mind Prelim. Obj 1: − ( a − b ) = b − a *************** Which are equivalent to − x − 1 x − 6 Answer choices: − x − 1 − x + 6 − x − 1 6 − x 1 − x x − 6 x − 1 − x + 6 None are equivalent Which are equivalent to − x + z x − z Answer choices: x + z z − x − x + z − x − z z + x − x + z − z − x x − z None are equivalent 2 Objective 1b Multiply/Divide Rational Expressions *************** Plan of Attack Factor Everything! Three types of factoring: Factor a trinomial; Always factor it . Use the hints provided by the other factors....
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Obj1thru8F11 - MAC 1105 Lecture Outlines for Ms...

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